Table 2.

Sorption kinetics models and their linear and non-linear forms with corresponding plots.

Model	Non linear	Linear	Parameter	Plot
Pseudo first order	$q_t=q_e\left(1,-,e^{-k_{1}t}\right)$	$log\left[q_e,-,q_t\right]=log{q}_e-\left[\frac{k_1}{2.303}\right]t$	k1 (min−1): rate constant for pseudo first order qe (mg g−1): sorption capacity at equilibrium qt (mg g−1): Sorption capacity at time “t”	$log\left[q_e,-,q_t\right]$ vs $t$
Pseudo second order	$q_t=\frac{\left(k_2,q_e^2,.,t\right)}{\left(1,+,k_2,q_e^2,.,t\right)}$	$\frac{t}{q_t}=\frac{1}{k_2{\left(q_e\right)}^2}+\frac{1}{q_e}\left(t\right)$	k2 (g mg−1 min−1): rate constant for pseudo first order	$\frac{t}{q_t}$ vs $t$
Elovich	$q_t=\beta ln\left(\alpha ,\beta ,t\right)$	$q_t=\frac{1}{\beta }ln\left[\alpha ,\beta \right]+\frac{1}{\beta }ln\left[t\right]$	α (mgg−1 min−1): rate of sorption process β (gmg−1): activation energy for chemical sorption process	$q_t$ vs $ln\left[t\right]$
Intraparticle diffusion	$q_t=K_{\mathit{ip}}{t}^{0.5}$	$q_t=K_{\mathit{ip}}{t}^{0.5}+I$	Kip (mg g−1 min0.5): constant for intraparticle diffusion I (mg g−1): constant related with thickness of boundary layer	$q_t$ vs $t^{0.5}$
Liquid film diffusion	–	$ln\left[1,-,F\right]=-k_{\mathit{fd}}\left(t\right)$	F: (qt/qe): fractional attainment of equilibrium kfd (min−1): rate constant of liquid film diffusion	$-ln\left[1,-,F\right]$ vs $t$